1
GATE CSE 2015 Set 3
+1
-0.3
Let $$\ne$$ be a binary operator defined as $$X \ne Y = X' + Y'$$ where $$𝑋$$ and $$𝑌$$ are Boolean variables. Consider the following two statements. \eqalign{ & \left( {S1} \right)\,\,\,\,\,\,\,\left( {P \ne Q} \right) \ne R = P \ne \left( {Q \ne R} \right) \cr & \left( {S2} \right)\,\,\,\,\,\,\,Q \ne R = R \ne Q \cr}\$

Which of the following is/are true for the Boolean variables $$𝑃, 𝑄$$ and $$𝑅$$?

A
Only $$S1$$ is true
B
Only $$S2$$ is true
C
Both $$S1$$ and $$S2$$ are true
D
Neither $$S1$$ nor $$S2$$ are true
2
GATE CSE 2014 Set 2
+1
-0.3
The dual of a Boolean function $$F\left( {{x_1},{x_2},\,....,\,{x_n},\, + , \cdot ,'} \right),$$ written as $${F^D}$$, is the same expression as that of $$F$$ with $$+$$ and $$\cdot$$ swapped. $$F$$ is said to be self-dual if $$F = {F^D} \cdot$$. The number of self-dual functions with $$n$$ Boolean variables is
A
$${2^n}$$
B
$${2^{n - 1}}$$
C
$${2^{{2^n}}}$$
D
$${2^{{2^{n - 1}}}}$$
3
GATE CSE 2014 Set 3
+1
-0.3
Consider the following combinational function block involving four Boolean variables $$x, y, a,$$
$$b$$ where $$x, a, b$$ are inputs and $$y$$ is the output.
Which one of the following digital logic blocks is the most suitable for implementing this function?
A
B
Priority encoder
C
Multiplexer
D
Flip-flop
4
GATE CSE 2014 Set 1
+1
-0.3
Consider the following Boolean expression for $$F:$$
$$F\left( {P,\,Q,\,R,\,S} \right) = PQ + \overline P QR + \overline P Q\overline R S.$$
The minimal sum-of-products form of $$F$$ is
A
$${PQ} + QR + QS$$
B
$$P + Q + R + S$$
C
$$\overline P + \overline Q + \overline R + \overline S$$
D
$$\overline P R + \overline P \overline R S + P$$
GATE CSE Subjects
EXAM MAP
Medical
NEET